This article is cited in 3 papers

The Cohomology of Pro-$p$-Groups with Group Ring Coefficients and Virtual Poincare Duality

A. A. Korenev

Belarusian State University

Abstract: The relationship between the group-theoretic properties of a pro-$p$-group $G$ and the $G$-module structure of the group $H^n(G,\mathbb F_q[[G]])$ is studied. A necessary and sufficient condition for a pro-$p$-group $G$ to contain an open Poincare subgroup of dimension $n$ is obtained. This condition does not require that $G$ have finite cohomological dimension and, therefore, applies to groups with torsion. Results concerning the possible values of $\dim_{\mathbb F_p}H^n(G,\mathbb F_p[[G]])$ are also obtained.

UDC: 512.546.37

Received: 29.04.2004

DOI: 10.4213/mzm2657

 English version: Mathematical Notes, 2005, 78:6, 791–800

Bibliographic databases:

• 
• 
• 
• 
•